% arara: indent: {overwrite: true, silent: on}
\documentclass[png,border=10pt,tikz]{standalone}
\usepackage{xstring}
\usepackage{tikz}
\usetikzlibrary{calc}

\pgfkeys{/tikz/.cd,
	vertical factor/.initial=0.5,
	vertical factor/.get=\vertfactor,
	vertical factor/.store in=\vertfactor,
	start coordinate/.initial={0,\vertfactor},
	start coordinate/.get=\startcoord,
	start coordinate/.store in=\startcoord,
	sample color/.initial=black,
	sample color/.get=\samplecol,
	sample color/.store in=\samplecol,
	sample size/.initial=1pt,
	sample size/.get=\samplesize,
	sample size/.store in=\samplesize,
	sample line width/.initial=very thick,
	sample line width/.get=\samplelinewidth,
	sample line width/.store in=\samplelinewidth,
}


\newcommand{\samplepath}[1]{%
	\coordinate (start) at (\startcoord) ;
	\foreach \samples[count=\xi from 1] in {#1}{%
		\StrCut{\samples}{|}{\vertdir}{\hordir}
		\ifnum\xi=1
			\draw[\samplelinewidth,\samplecol](start)
			--++(\hordir,0) coordinate (start);
		\else
			\IfStrEq{\vertdir}{+}{%true
				\draw[\samplelinewidth,\samplecol]($(start)+(0,\vertfactor)$)
				--++(\hordir,0)coordinate(start);
				}{%false
				\relax
			}
			\IfStrEq{\vertdir}{-}{%true
				\draw[\samplelinewidth,\samplecol]($(start)+(0,-\vertfactor)$)
				--++(\hordir,0)coordinate(start);
				}{%false
				\relax
			}
		\fi
	}
}

\tikzset{sample/.style={
	circle,
	inner sep=\samplesize,
	fill=\samplecol,
	}
}

\newcommand{\discretesamplepath}[1]{%
	\coordinate (start) at (\startcoord) ;
	\foreach \samples[count=\xi from 1] in {#1}{%
		\StrCut{\samples}{|}{\vertdir}{\hordir}
		\ifnum\xi=1
			\path(start)node[sample]{}
			--++(\hordir,0) coordinate (start);
		\else
			\IfStrEq{\vertdir}{+}{%true
				\path($(start)+(0,\vertfactor)$)node[sample]{}
				--++(\hordir,0)coordinate(start);
				}{%false
				\relax
			}
			\IfStrEq{\vertdir}{-}{%true
				\path($(start)+(0,-\vertfactor)$)node[sample]{}
				--++(\hordir,0)coordinate(start);
				}{%false
				\relax
			}
		\fi
	}
}

\begin{document}
\begin{tikzpicture}
	% axis
	\draw[-stealth] (0,-1)--(0,4) node[left]{$X(t)$};
	\draw[-stealth] (-1,0)--(5,0) node[below]{$t$};
	\samplepath{+|0.5,+|0.25,-|1.5,+|1,+|0.5,+|0.75}
\end{tikzpicture}
\end{document}
